Enhanced descriptions from Syndetics:

Sophie, who helps out at her late father's hat shop, is transformed one day by a witch into an old woman. Sophie seeks out the help of the wizard Howl, who has an amazing moving castle which is fueled by a fire demon named Calcifer.

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A young woman named Sophie is cursed by the Witch of the Waste and is turned into an old woman who is unable to tell anyone of her plight. Unable to continue her job at her mother's hat shop, she goes to the ambulatory castle of the notorious wizard Howl and insinuates herself into his household. Sophie befriends Calcifer, the fire demon who powers the castle and who is bound to Howl by a contract, the terms of which Calcifer cannot reveal. They promise to help each other with the their problems. Like Calcifer, Howl can also see through the Witch's spell, and he and Sophie fall in love. Sophie helps Howl confront his former teacher, and the Witch of the Waste.